How to interpolation between matrices

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Imagine the plot attached below. Each point on this plot represents a a 4x4 matrix that describes the behavior of the plant at that particular point. For a controller design, I have a reference load which I need to track at a given speed (omega).
How do I interpolate to get the specific 4-D matrix at a load point and speed which is not already a point on the plot?
Thanks!

Accepted Answer

Stephen23
Stephen23 on 29 Jul 2022
Assuming that you want to interpolate between the corresponding elements of those 4x4 matrices, then you could do something like this:
C = {randi(9,4,4), randi(9,4,4), randi(9,4,4)}; % 4x4 matrices in a cell array
C{:}
ans = 4×4
2 8 7 7 7 1 5 7 7 8 5 5 3 3 2 7
ans = 4×4
1 3 7 1 3 1 5 6 4 3 9 7 9 4 2 5
ans = 4×4
5 3 4 5 2 3 9 3 7 9 6 2 2 3 9 6
L = [1;3;2]; % load
W = [7;8;9]; % omega
M = cat(3,C{:});
[X,Y] = meshgrid(1:numel(C),1:16);
F = scatteredInterpolant(Y(:),L(X(:)),W(X(:)),M(:),'linear','linear');
Interpolate the entire matrix:
Lq = 1.5;
Wq = 7.5;
out = reshape(F({1:16,Lq,Wq}),4,4)
out = 4×4
2.3333 6.3333 6.5000 5.6667 5.5000 1.3333 5.6667 6.1667 6.5000 7.3333 5.8333 4.8333 3.8333 3.1667 3.1667 6.5000
Lq = 2;
Wq = 8;
out = reshape(F({1:16,Lq,Wq}),4,4)
out = 4×4
2.6667 4.6667 6.0000 4.3333 4.0000 1.6667 6.3333 5.3333 6.0000 6.6667 6.6667 4.6667 4.6667 3.3333 4.3333 6.0000
  2 Comments
Stephen23
Stephen23 on 30 Jul 2022
Edited: Stephen23 on 30 Jul 2022
"is the '3' in the concatenated line from having three matrices in C?"
No, it means that we concatenate those matrices along the third dimension.
"In other words, what would that number be if my cell array C contains 20 matrices?"
3

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